Please annotate each step so I don't have to guess what you're trying to do. :v Bracketed moves are done on inverse. (The bolded moves were wrongly written in your post and have been corrected here.)

(U2 R2 U2) // square (3/3)

(D F2 U D F2 D' F D L D' L' U2) // 223 (12/15)

(R' B R) // EO (3/18)

(D' B

**D** B') // F2L-1 (4/22)

B' D2 B D

**B' D B D B' D2 B** // OLS (11/33)

D F D F' D' F' R F2 D' F' D' F D F' R' // T perm (15/48)

The 223 is not great, considering that there's a free pair to exploit. Consider something like:

(U2 R2 U2) // pseudo222 (3/3)

(R' D F2) // pseudo223 (3/6)

U // fix pseudoblock (1/7)

This does leave six bad edges, which is unfortunate, but at least we can cancel into EO (which happens to also solve a square here—you can get unlucky in an early part of the solution and still get lucky later on).

U (U2 R2 U2 R' D F2) // 223 with six bad edges (7/7)

(F D' F2 B R F B') // EO + square (7-1/13)

(D2 R D R' D R D') // solve edges; leave four corners (7/20)

Going back to your solution:

(U2 R2 U2) // square (3/3)

(D F2 U D F2

**D' F D L D' L'** U2) // 223 (12/15)

The bolded moves can be replaced by D2 F L D L', which saves a move. (It also happens to cause an EO skip, but this was unintentional.) The first bolded D' move moves the green-orange edge out of the way so that you can insert green-red, but it's left in a position where you'll need four moves to insert it. By using D2 instead, it's left in a position that takes only three moves to insert.

… // 223

(R' B R) // EO (3/18)

(D' B D B') // F2L-1 (4/22)

Fairly obvious stuff here.

… // F2L-1

B' D2 B D B' D B D B' D2 B // OLS (11/33)

D F D F' D' F' R F2 D' F' D' F D F' R' // T perm (15/48)

Getting an OLL skip here is nice, but hoping for OLL skips isn't exactly a reliable strategy and also most PLLs aren't short enough to be useful in FMC. T perm is one of the few exceptions, and you should definitely learn the

optimal T perm algs. (You did say you didn't want to learn algs, but this one is really easy to remember!)

… // OLS

L2 U B2 U' L2 F2 U' R2 U F2 // optimal T perm (10/43)

An alternative to finishing F2L:

… // F2L-1

(B' D' B D B' D B D2) // solve edges; leave five corners (8-1/29)

Start learning how to do insertions asap. Being able to solve 4-5 corners in 11-ish moves is usually far better than spending 20+ moves on doing OLL and PLL. (Insertions aren't essential per se; roughly a third of my FMC attempts have no insertions at all. I do, however, know enough ZBLL and related stuff that I can get away with not doing insertions and still average 35 moves. This obviously isn't an option if you have an aversion to learning hundreds of algs.)